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QUADRILATERAL (Segiempat)

QUADRILATERAL (Segiempat). Base of Competence. Identify the propert ies of rectangle, square, parallelogram , rhombus, kite and trapezoid . Determine the perimeter and the area of quadrilateral and how to use it in problem solving

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QUADRILATERAL (Segiempat)

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  1. QUADRILATERAL(Segiempat)

  2. Base of Competence • Identify the properties of rectangle, square, parallelogram, rhombus, kite and trapezoid. • Determine the perimeter and the area of quadrilateral and how to use it in problem solving • Solving of problem which has relation with perimeter and area of quadrilateral

  3. B . A . . D . C QUADRILATERALS(General Properties) • 4vertices • 4 sides • 4 angles

  4. B . A . B . A . . D . . D C The sum of ALL the angles of a quadrilateral is 360o . C QUADRILATERALS(General Properties) 360o

  5. B . A . . D . C The sum of ALL the angles of a quadrilateral is 360o QUADRILATERALS(General Properties) 360o

  6. QUADRILATERALS(FOUR SIDED POLYGON) CLASSIFICATION OF QUADRILATERAL PARALLELOGRAM RHOMBUS SQUARE RECTANGLE TRAPEZOID ISOSCELES TRAPEZOID

  7. 1. RECTANGLE Which is rectangle ? 1 3 2 4 5 6

  8. RECTANGLE IN OUR SUROUNDING

  9. B A D C C B D A 7. Consecutive angles are supplementary. + + + + = = = = 180° 180° 180° 180° Has two pairs of parallel sides. (AB // DC; AD // BC) AB and DC; AD and BC are pairs of opposite sides THE PROPERTIES RECTANGLE A B 2. Has two pairs of congruent sides. 3. All angles are right angle. D C 4. All diagonals are congruent 5. All diagonals bisect each other 8. Has two axis of simmetry 6. Opposite angles are congruent. 9. Has rotational simmetry order 2 10. Can fits its frame in 4 ways

  10. R S RSTU is a Rectangle 7x+3 RQ =7x + 3 QT = 9x – 13 Q 9x – 13 Find the value for xandQS. U T In a rectangle diagonals bisect each other, then: Since all four segments formed when the diagonals bisect are congruent, finding one we’ll know the value for all. 7x+ 3 = 9x – 13 RQ = 7x + 3 3+13= 9x – 7x = 7( ) + 3 8 16 = 2x = 56 + 3 x=8 = 59 RQ = TQ = QS = UQ The length of QS is 59.

  11. A B ABCD is a Rectangle 3x+5 BQ =3x + 5 CQ = 6x – 10 Q 6x – 10 Find the value for x and DQ. D C In a rectangle diagonals bisect each other, then: Since all four segments formed when the diagonals bisect are congruent, finding one we’ll know the value for all. 3x + 5 = 6x – 10 BQ = 3x + 5 5 + 10= 6x – 3x =3( ) + 5 5 15 = 3x = 15 + 5 x=5 = 20 BQ = DQ = AQ = CQ The length of DQ is 20.

  12. length width width length PERIMETER AND AREA Perimeter Perimeterof a shape is the total length of its sides. Perimeter of a rectangle = length + width + length + width P = l + w + l + w P = 2l + 2w P = 2(l + w)

  13. 1 metre 1 cm 1 mm 1 mm 1 metre 1 cm Area Area measures the surface of something. 1mm2 1m2 1cm2 1 square metre

  14. 5 metres long 3 metres wide Area of a rectangular lawn 15 square metres = 15 m2 The area is Area of a rectangle = Length x Width

  15. Example • The length and the width of a rectangle is enlarge 3 times. Find the ratio of: a. Original area to new area b. Original perimeter to new perimeter 2. The length of a rectangle is enlarge 2 times and the width is enlarge 3 times. Find the ratio of original area to new area.

  16. The length of a rectangle is enlarge 2 times and the width is decrease ½ than original width. Find the ratio of original area to new area. (1 : 2 x ½ ) = (1 : 1) • The length of a rectangle is decreased 1/3 times and the length is enlarge 6 times. Find the ration of original area to new area. ( 1 : 1/3 x 6) = 1 : 2 • The length of rectangle is changed to 1/3 than the original and the width is changed to ½ than the orginal. The ratio of original area to new area is ... ( 1 : 1/3 x ½ = 1 : 1/6 = 6 : 1)

  17. Example The length and the width of rectangle are 15 cm and 12 cm respectively. Find the perimeter and the area of rectangle. The ratio of rectangle’s length and width is 5 : 3, if the perimeter of the rectangle is 64 cm find the length and the width of the rectangle. The perimeter of rectangle is 80 cm. If the length is 4 cm more than the width, find the length and the width of the rectangle.

  18. Example 4. The area of the rectangle is 420 cm2. If the length is 21 cm find the length of its diagonal. The perimeter of a rectangle is 44 cm. The difference of its length and width is 6 cm. Find the area of the rectangle. The ratio of rectangle’s length and width is 7 : 5, if the area of the rectangle is 315 cm2, then find the perimeter of the rectangle. The length of the rectangle enlarge 5 times and the width is enlarge 3 times. The ratio of original area to new area is ....

  19. B D C C D B A A 8. Consecutive angles are supplementary. + + + + = = = = 180° 180° 180° 180° SQUARE 1. Two pairs of parallel sides. AB//DC, AD// BC A B 2. All sides are congruent. 3. All angles are right. 4. Diagonals are congruent 5. Diagonals intersect and bisecteach other D C 6. Diagonals are perpendicular 7. Opposite angles are congruent. 9. It has 4 axis simmetry 10. It has rational simmetry order 4 11. It can fits its frame in 8 ways

  20. CHECK UNDERSTANDING

  21. OLM UV = ..... VX = .....

  22. 8 cm 4 cm (3x-2) cm 1. Look at the figures on the right. If the area of the square is equal to the area of the rectangle, then the perimeter of the rectangle is .... a. 20 cm b. 32 cm c. 40 cm d. 64 cm 2. The perimeter of a rectangle is 38 cm. If the difference of the length and the width is 5 cm, then the length of the rectangle is .... a. 12 cm b. 10 cm c. 9 cm d.7 cm

  23. Problem Solving 1 D C ABCD is a square. If BD = 12 cm, find the area of square ABCD A B

  24. Problem Solving 1 Mr Ahmad has a rectangular pool with the measure of 20 m x 10 m. Around the outside of the pool will make a path with the width of 1 m. The path will wraped with ceramics. If the price of 1 m2 ceramics is Rp 60,000.00, how much money does Mr. Ahmad needs?

  25. Problem Solving 3 D C ABCD is a square. If AB = 6 cm and EF : BD = 1 : 3 Then find the area of the shaded region. (EFC) E F A B

  26. Problem Solving 4 R S M N P Q PQRS is a rectangle. If PQ = 20 cm, QR = 15 cm and MN =½SQ Then find the area of the shaded region. (PNRM)

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